Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

sample1.8s

Algorithm

intervals

Results

1.7s	139×	body	5120	exit
76.0ms	256×	body	80	valid
6.0ms	398×	pre	80	true
1.0ms	3×	body	80	invalid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4652	74
1	4652	74

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.8b

Counts

2 → 2

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
56×	`frac-add_binary64`
41×	`distribute-lft-out_binary64` `sum-log_binary64`
13×	`flip3-+_binary64` `flip-+_binary64`
7×	`pow1_binary64`
4×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`associate-+l+_binary64` `+-commutative_binary64`
2×	`sqrt-pow1_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-prod_binary64`

Counts

4 → 90

Calls

4 calls:

47.0ms	(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
92.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
25.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

series25.0ms

Counts

4 → 10

Calls

4 calls:

8.0ms	(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
13.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
4.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

simplify76.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4995	6097
1	4995	6097

prune580.0ms

Filtered

72 candidates to 100 candidates (-38.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 0.3b

Counts

102 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 z)
0.4b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`
9×	`times-frac_binary64`
8×	`prod-exp_binary64`
7×	`associate-r_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-/l_binary64`
2×	`sqrt-pow1_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `pow-sub_binary64` `exp-sum_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `associate-l/_binary64`

Counts

4 → 77

Calls

4 calls:

6.0ms	(*.f64 PI.f64 z)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series31.0ms

Counts

4 → 10

Calls

4 calls:

2.0ms	(*.f64 PI.f64 z)
7.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
21.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4999	973
1	4999	973

prune131.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	82	11	93

Merged error: 0.0b

Counts

93 → 11

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
1.0b	(*.f64 (pow.f64 PI.f64 4) 7/360)
1.6b	(pow.f64 PI.f64 4)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
8×	`associate-l_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`pow-prod-down_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `associate-r/_binary64` `pow-pow_binary64` `pow-sub_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `associate-l/_binary64`

Counts

4 → 74

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
5.0ms	(*.f64 (pow.f64 PI.f64 4) 7/360)
2.0ms	(pow.f64 PI.f64 4)

series21.0ms

Counts

4 → 6

Calls

4 calls:

21.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(*.f64 (pow.f64 PI.f64 4) 7/360)
0.0ms	(pow.f64 PI.f64 4)

simplify73.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4932	947
1	4932	947

prune140.0ms

Filtered

54 candidates to 80 candidates (-48.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	80	11	91

Merged error: 0.0b

Counts

91 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 z)
0.4b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
14×	`pow1_binary64`
13×	`prod-exp_binary64`
9×	`times-frac_binary64`
7×	`cbrt-unprod_binary64`
6×	`associate-r_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`sqrt-pow1_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `pow-sub_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64` `pow-exp_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(*.f64 PI.f64 z)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
17.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series38.0ms

Counts

4 → 10

Calls

4 calls:

2.0ms	(*.f64 PI.f64 z)
7.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
28.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify68.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4942	981
1	4942	981

prune87.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	89	11	100

Merged error: 0.0b

Counts

100 → 11

regimes62.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	57
1	77	57

end0.0ms

sample48.6s

Algorithm

intervals

Results

45.6s	3783×	body	5120	exit
2.5s	8000×	body	80	valid
197.0ms	11870×	pre	80	true
28.0ms	87×	body	80	invalid

Details

analyze1.7s

sample1.8s

simplify42.0ms

prune13.0ms

localize52.0ms

rewrite174.0ms

series25.0ms

simplify76.0ms

prune580.0ms

localize30.0ms

rewrite31.0ms

series31.0ms

simplify45.0ms

prune131.0ms

localize45.0ms

rewrite29.0ms

series21.0ms

simplify73.0ms

prune140.0ms

localize32.0ms

rewrite30.0ms

series38.0ms

simplify68.0ms

prune87.0ms

regimes62.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample48.6s

Profiling